Four students drive to school in the same car. The students claim they were late

Question

Four students drive to school in the same car. The students claim they were late to school and missed a test because of a flat tire. Each student is asked one at a time, separately and independently, which tire was flat; front driver's side, front passenger side, rear driver's side, or rear passenger's side. If the students didn't really have a flat tire and each independently and randomly selects a tire, what is the probability that all four students select the same tire? A Latin multiple-choice test has three questions, each with five choices for the answer. Only one of the choices is correct for each problem. You did not study Latin, so you randomly and independently guess the answer to each question. What is the probability that you answer at least one of the questions correctly?

Explanation / Answer

#5

There are 4^4 possibilities for their choices. (The first student has 4 choices, as do the second, third and fourth, for 4^4 total.) There are four possibilities where they all select the same tire -- one possibility for each tire. Therefore the probability that they all select the same tire is 4/4^4 = 1/4^3 = 1/64.

#6

A multiple choice quiz has three questions, each with five answer choices. Only one of the choice is correct. The probability of correct answer of each question is 1/5.

Therefore, the probability of incorrect answer of each question is 4/5.

The probability of answering none of the questions correctly.
(4/5)^3 = 0.512

The probability if answering at least one of the questions correctly is:

P(at least one correct)=1-P(none correct) = 1 - 0.512 = 0.488

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